Abstract
A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed.
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Rosenthal, J. Probabilities as Ratios of Ranges in Initial-State Spaces. J of Log Lang and Inf 21, 217–236 (2012). https://doi.org/10.1007/s10849-011-9153-x
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DOI: https://doi.org/10.1007/s10849-011-9153-x